Step: 1

Area of a triangle = 1 2 × base × height

Step: 2

= 1 2 × 5 × 6

[Substitute base = 5 and height = 6.]

Step: 3

= 30 2 = 15

[Simplify.]

Step: 4

The area of the triangle is 15 in^{2}.

Correct Answer is : 15 in^{2}

Step: 1

Area of the triangle = 1 2 × base × height

Step: 2

The height of the triangle is two times the length of the base.

Step: 3

Height of the triangle = 2 × base length = 2 × 9 = 18 m

[Substitute base length = 9.]

Step: 4

Area of the triangle = 1 2 × 9 × 18

[Substitute the values.]

Step: 5

= 9 × 9 = 81

[Simplify.]

Step: 6

The area of the triangle is 81 m^{2}.

Correct Answer is : 81 m^{2}

Step: 1

The area of the triangle = 1 2 × base × height

[Formula.]

Step: 2

The base length = 3 × height

= 3 × 6 = 18 ft

= 3 × 6 = 18 ft

[Since base is three times the height.]

Step: 3

So, area of the triangle = 1 2 × 18 × 6

[Substitute the values.]

Step: 4

= 108 2

[Simplify.]

Step: 5

= 54 ft^{2}

[Divide the numerator and the denominator by 2.]

Step: 6

Area of the triangle = 54 ft^{2}.

Correct Answer is : 54 ft^{2}

Step: 1

Area of the shaded region of the figure = area of the triangle ABC - area of the triangle DEF

Step: 2

Area of a triangle with base b and height h = 1 2 × b × h

Step: 3

The area of the triangle ABC = 1 2 × BC × height of the triangle ABC = 1 2 × 6 × 5.

[Substitute BC = 6 cm and height = 5 cm.]

Step: 4

= 30 2 = 15 cm^{2}

[Simplify.]

Step: 5

The area of the shaded region of the figure = 15 - 5

[Substitute the areas of the triangles.]

Step: 6

= 10 cm^{2}

[Subtract.]

Step: 7

The area of the shaded region of the figure = 10 cm^{2}.

Correct Answer is : 10 cm^{2}

Step: 1

In the figure, BY = YC = BC 2 = 8 2 = 4 m

[Since Y is the midpoint of BC.]

Step: 2

Area of the parallelogram XBYZ = base x height = BY × XP

Step: 3

= 4 × 2 = 8 m^{2}

[Substitute BY = 4 and XP = 2.]

Step: 4

Area of the shaded region = Area of the triangle ABC - Area of the parallelogram XBYZ

Step: 5

= 16 - 8 = 8 m^{2}

[Substitute and subtract.]

Correct Answer is : 8 m^{2}

Step: 1

Let h is the height of the triangle.

Step: 2

Given, area of the triangle = 225 yd^{2}

The base = twice the height = 2 ×h .

The base = twice the height = 2 ×

Step: 3

Area of a triangle = 1 2 × base × height

[Formula.]

Step: 4

225 = 1 2 × 2 × h × h

[Substitute the values.]

Step: 5

225 = h ^{2}

[Simplify.]

Step: 6

[Taking square root on both sides.]

Step: 7

15 = h

Step: 8

The height of the triangle = 15 yd.

Correct Answer is : 15 yd

Step: 1

Base of the triangle = 12 in. and the height of the triangle = 5 in.

[Figure.]

Step: 2

The area of ΔABC = 1 2 × base × height

[Formula.]

Step: 3

= 1 2 × 12 × 5

[Substitute the values.]

Step: 4

= 30

[Multiply.]

Step: 5

The area of the triangle ABC = 30 in.^{2}

Step: 6

Area of the circle = π (d 2 )^{2}

[Formula.]

Step: 7

= 3.14 × (12 2 )^{2}

[Substitute the values.]

Step: 8

= 3.14 × 6^{2}

Step: 9

= 113.04

[Simplify.]

Step: 10

The area of the circle = 113.04 in.^{2}

Step: 11

Area of the shaded region = area of the circle - area of the triangle ABC

Step: 12

= 113.04 - 30

[From Steps 5 and 10.]

Step: 13

= 83.04

Step: 14

So, the area of the shaded region is 83.04 in.^{2}

Correct Answer is : 83.04 in.^{2}

Step: 1

From the figure, base of the triangle is 2 units, and its height is 3 units.

Step: 2

Area of triangle = 1 2 × base × height

[Formula.]

Step: 3

Area of the triangle ABC

= 1 2 × 2 × 3

[Substitute the values.]

Step: 4

= 3 square units

Step: 5

Area of the triangle ABC = 3 square units.

Correct Answer is : 3 square units

Step: 1

Area of a triangle with base b and height h = 1 2 × b × h

Step: 2

From the figure, base of the triangle = BC = 32 ft and height of the triangle = AB = 24 ft

Step: 3

Area of the triangle ABC = 1 2 × 32 ft × 24 ft = 384 ft^{2}

[Substitute the values and simplify.]

Step: 4

The area of the triangle = 384 ft^{2}.

Correct Answer is : 384 ft^{2}

Step: 1

Base of the triangle is 9 cm and its height is 40 cm.

Step: 2

Area of a triangle = 1 2 × base × height

Step: 3

= 1 2 × 9 × 40

Step: 4

= 180

Step: 5

Area of the triangle is 180 cm^{2}.

Correct Answer is : 180 cm^{2}

Step: 1

Base of the triangle is 35 cm and height is 16 cm.

Step: 2

Area of a triangle = 1 2 × base × height

Step: 3

= 1 2 × 35 × 16

Step: 4

= 280

[Simplify.]

Step: 5

So, area of the triangle is 280 cm^{2}.

Correct Answer is : 280 cm^{2}

- Areas of Composite Plane Figures-Gr 6-Solved Examples
- Net Figures made up of Rectangles and Triangles-Gr 6-Solved Examples

- Area